Maximal regularity, the local inverse function theorem, and local well-posedness for the curve shortening flow

Sahbi Boussandel; Ralph Chill; Eva Fašangová

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 2, page 335-346
  • ISSN: 0011-4642

Abstract

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Local well-posedness of the curve shortening flow, that is, local existence, uniqueness and smooth dependence of solutions on initial data, is proved by applying the Local Inverse Function Theorem and L 2 -maximal regularity results for linear parabolic equations. The application of the Local Inverse Function Theorem leads to a particularly short proof which gives in addition the space-time regularity of the solutions. The method may be applied to general nonlinear evolution equations, but is presented in the special situation only.

How to cite

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Boussandel, Sahbi, Chill, Ralph, and Fašangová, Eva. "Maximal regularity, the local inverse function theorem, and local well-posedness for the curve shortening flow." Czechoslovak Mathematical Journal 62.2 (2012): 335-346. <http://eudml.org/doc/246132>.

@article{Boussandel2012,
abstract = {Local well-posedness of the curve shortening flow, that is, local existence, uniqueness and smooth dependence of solutions on initial data, is proved by applying the Local Inverse Function Theorem and $L^2$-maximal regularity results for linear parabolic equations. The application of the Local Inverse Function Theorem leads to a particularly short proof which gives in addition the space-time regularity of the solutions. The method may be applied to general nonlinear evolution equations, but is presented in the special situation only.},
author = {Boussandel, Sahbi, Chill, Ralph, Fašangová, Eva},
journal = {Czechoslovak Mathematical Journal},
keywords = {curve shortening flow; maximal regularity; local inverse function theorem; curve shortening flow; maximal regularity; local inverse function theorem},
language = {eng},
number = {2},
pages = {335-346},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Maximal regularity, the local inverse function theorem, and local well-posedness for the curve shortening flow},
url = {http://eudml.org/doc/246132},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Boussandel, Sahbi
AU - Chill, Ralph
AU - Fašangová, Eva
TI - Maximal regularity, the local inverse function theorem, and local well-posedness for the curve shortening flow
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 2
SP - 335
EP - 346
AB - Local well-posedness of the curve shortening flow, that is, local existence, uniqueness and smooth dependence of solutions on initial data, is proved by applying the Local Inverse Function Theorem and $L^2$-maximal regularity results for linear parabolic equations. The application of the Local Inverse Function Theorem leads to a particularly short proof which gives in addition the space-time regularity of the solutions. The method may be applied to general nonlinear evolution equations, but is presented in the special situation only.
LA - eng
KW - curve shortening flow; maximal regularity; local inverse function theorem; curve shortening flow; maximal regularity; local inverse function theorem
UR - http://eudml.org/doc/246132
ER -

References

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